The difference is that #define is processed by the preprocessor doing what amounts to simple text replacement. Const values defined like this are not visible for the actual compiler, while a variable defined with the const modifier is an actual typed "variable" (well not really that variable). The disadvantage of #define is that is replaces every occurence of the name, while const variables get normal lookup, so you have less risk of naming conflicts and it's not typesafe.
The advantage of #define is that it guarantees constness and therefore there will be no backing variable. Const Variables may or may not be substituted into the code, so #define might be faster in some situations. However a good compiler should inline those consts anyways and it's unlikely to make much of a difference in most situations, so I would keep using const unless you have a piece of code where you have seen that the compiler hasn't inlined the variable and it is very, very performance critical code.
